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One plausible thesis, stated using plural quantification, is that there are some things that are all things. Although widely accepted, in this chapter it is argued that that thesis is false. The argument involves three plausible claims: (1) There are two or more things; (2) for any things, there is a unique thing to which they correspond; (3) for any two or more things, there are fewer of them than there are pluralities of them. The first claim is obvious. Certain metaphysical views about the nature of propositions support the second. The third follows from a plural version of Cantor's...

One plausible thesis, stated using plural quantification, is that there are some things that are all things. Although widely accepted, in this chapter it is argued that that thesis is false. The argument involves three plausible claims: (1) There are two or more things; (2) for any things, there is a unique thing to which they correspond; (3) for any two or more things, there are fewer of them than there are pluralities of them. The first claim is obvious. Certain metaphysical views about the nature of propositions support the second. The third follows from a plural version of Cantor's Theorem and holds even in cases involving infinity. The argument from these three claims to the denial of the widely accepted thesis is explained and defended in this chapter. The conclusion of this argument has widespread ramifications in mereology, quantification, and theories of truth.